A.6 
The student will graph linear equations and linear inequalities in two variables, including
a) determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined. 

Essential Knowledge and Skills 
 Find the slope of the line, given the equation of a linear function.
 Find the slope of a line, given the coordinates of two points on the line.
 Find the slope of a line, given the graph of a line.
 Recognize and describe a line with a slope that is positive, negative, zero, or undefined.

Essential Understandings 
 Changes in slope may be described by dilations or reflections or both.
 The slope of a line represents a constant rate of change in the dependent variable when the independent variable changes by a constant amount.
 The product of the slopes of perpendicular lines is 1 unless one of the lines has an undefined slope.


Vertical Articulation 
 SOL 7.15  a) solve onestep inequalities; b) graph solutions on number line
 SOL 8.15  b) solve twostep linear inequalities and graph results on number line; c) identify properties of operations used to solve
 SOL 8.16  graph linear equations in two variables
 SOL AFDA.2  use transformations to write equations, given graph of function (linear/quad/exponential/log)
 SOL AII.6  recognize general shape of function (absolute value/square root/cube root/rational/poly/exponential/ log) families/ convert between graphic and symbolic forms of functions ‐ transformational approach to graphing

Instructional Materials 
 VDOE ESS Lesson: Slope2Slope  Equations and Inequalities (PDF)  Investigating slope of horizontal and vertical lines and graphing a line (Word)
 VDOE ESS Lesson: Slippery Slope  Equations and Inequalities (PDF)  Writing equations of lines (Word)
 VDOE ESS Lesson: The Submarine  Equations and Inequalities (PDF)  Investigating slope as rate of change (Word)
 VDOE ESS Lesson: Equations of Lines  Equations and Inequalities (PDF)  Writing equations of lines (Word)
 Notes: Graphing and Transforming Linear Equations (doc)  Answer Key (pdf)

Real World Lessons 
 Den Meyer: Joulies  Do you think Joulies will work as advertised?
 Mathalicious: Can Music Kill You?  Is there a relationship between music tempo and heart rate?
 Mathalicious: Datelines  Is the "half plus seven" rule for MayDecember relationships a good one?
 Mathalicious: Domino Effect  How much is Domino's really charging you for pizza…and toppings?
 Mathalicious: Donut Stand  What does a little donut stand in Virginia have to do with rates of change, limits, average and marginal cost?

Practice 
 VDOE ESS: Silent Bingo Game (pdf)
 VDOE ESS: Slope2Slope Puzzle (pdf)  Answer Key (pdf)
 VDOE ESS: SlopeIntercept Cards (pdf)
 Worksheet: Graphing and Transforming Linear Equations CW (doc)
 Worksheet: Graphing and Transforming Linear Equations HW (doc)

SelfAssessments 
 SOL Mini Quiz

Skills 
 Mathematics Assessment Project: A17:Linear Graphs  Apprentice  In this task, you are asked to match equations with linear graphs.
 JMU Pivotal Question: Determine Ordered Pairs Given Slope (doc)
 JMU PIvotal Question: Graphing  Is Claire Correct? (doc)
 JMU Pivotal Question: Parallel Lines (doc)

Videos 
 Video: PH Graphing an equation Using SlopeIntercept Form
 Video: PH Graphing Using PointSlope Form

Explore
Learning 
 DistanceTime and VelocityTime Graphs  Create a graph of a runner's position versus time and watch the runner run a 40yard dash based on the graph you made. Notice the connection between the slope of the line and the velocity of the runner. Add a second runner (a second graph) and connect realworld meaning to the intersection of two graphs. Also experiment with a graph of velocity versus time for the runners, and also distance traveled versus time.
 Function Machines 2 (Functions, Tables, and Graphs)  Drop a number into a function machine, and see what number comes out! You can use one of the six preset function machines, or program your own function rule into one of the blank machines. Stack up to three function machines together. Input and output can be recorded in a table and on a graph.
 Modeling Linear Systems  Activity A  Experiment with a system of two lines representing a cat‑and‑mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real‑world meaning to slope, y‑intercept, and the intersection of lines.
 Slope  Activity B  Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes.

Websites 
 Interactive
Notes: Graphing Linear Equations  lessons
and practice problems at Regentsprep.org
 Notes:
Graphing Using Slope and Yintercept 
notes on graphing using slope and yintercept at Purplemath.com
 Notes:
Writing Equations of Lines  notes on finding
the slope at Purplemath.com
 Interactive
Notes: Writing Equations of Lines  lessons
and practice problems at Regentsprep.org
 Interactive:
Slope Slider  manipulate a linear function
in the form of f(x) = mx + b at Shodor.org.
 Interactive: Exploring SlopeIntercept Form  mathlet from GeoGebra
 Interactive: Investigating Horizontal Lines  mathlet from GeoGebra
 Interactive: Investigating Vertical Lines  mathlet from GeoGebra

Old Website Links 

Common Core
Standards 
8.EE.5 
8.EE.6 
8.F.3 
8.F.4 
8.SP.3 
ACED.2 
AREI.10 
AREI.12 
FIF.6 
FBF.3 
FLE.2 
SID.7 
